University of Primorska Faculty of Mathematics, Natural Sciences and Information Technologies
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Mathematical Research Seminar - Archive

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Datum in ura / Date and time: 29.4.24
(15:00 -- 16:00)
Predavalnica / Location: FAMNIT-MP1
Predavatelj / Lecturer: Aljaž Kosmač (University of Primorska)
Naslov / Title: Isogeometric collocation for solving the biharmonic equation over planar multi-patch domains
Vsebina / Abstract:
 
We present an isogeometric collocation method for solving the biharmonic equation over planar bilinearly parameterized multi-patch domains. The developed approach
is based on the use of the globally $C^4$-smooth isogeometric spline space [Kapl, Vitrih, 2021] to approximate the solution of the considered partial differential equation, and proposes as collocation points two different choices, namely on the one hand the Greville points and on the other hand the so-called superconvergent points. Several examples demonstrate the potential of our collocation method for solving the biharmonic equation over planar multi-patch domains, and numerically study the convergence behavior of the two types of collocation points with respect to the $L^2$-norm as well as to equivalents of the $H^s$-seminorms for $1 \leq s \leq 4$.
 
In the studied case of spline degree $p=9$, the numerical results indicate in case of the Greville points a convergence of order $\mathcal{O}(h^{p-3})$ independent of the considered (semi)norm, and show in case of the superconvergent points an improved convergence of order $\mathcal{O}(h^{p-2})$ for all (semi)norms except for the equivalent of the $H^4$-seminorm, where the order $\mathcal{O}(h^{p-3})$ is anyway optimal. 
 
Joint work with M. Kapl (Carinthia University of Applied Sciences, Villach, Austria) and V.Vitrih (IAM, University of Primorska).
Datum in ura / Date and time: 22.4.24
(15:00-16:00)
Predavalnica / Location: FAMNIT-MP1
Predavatelj / Lecturer: Tomaž Pisanski (University of Primorska, Slovenia)
Naslov / Title: Geometric symmetry of graphs
Vsebina / Abstract:

This work in progress explores graphs that can be drawn in the Euclidean plane exhibiting non-trivial geometric symmetry. We investigate the significance of semiregular and quasi-semiregular automorphisms for achieving such symmetric embeddings. We consider both cyclic and dihedral symmetries.

Datum in ura / Date and time: 15.4.24
(9:50-16:30)
Predavalnica / Location: FAMNIT-VP1
Predavatelj / Lecturer: Marston Conder (University of Auckland, New Zeland)
Naslov / Title: Magma Mini-Course
Vsebina / Abstract:

Get ready for an exhilarating opportunity this April!  Professor Marston Conder from New Zealand will grace FAMNIT with his presence to deliver an insightful mini-course on MAGMA, the powerful computational algebra system.

Course Outline:
Overview of MAGMA and its applications, including graphs, digraphs, and Cayley graphs.
Handling permutation groups, matrix groups, and groups of small order.
Exploring finitely presented groups and their practical applications.

Plus, exciting demonstrations showcasing the practical usage of MAGMA will be included!

Mark your calendars! Here's the schedule:


Monday, April 15th: FAMNIT-VP1
- Opening: 9:50 - 10:00
- MAGMA 1: 10:00 - 11:00
- Coffee break: 11:00 - 11:30
- MAGMA 2: 11:30 - 12:30
- Lunch: 12:30 - 14:00
- MAGMA 3: 14:00 - 15:00
- Coffee break: 15:00 - 15:30
- MAGMA 4: 15:30 - 16:30

Tuesday, April 16th:FAMNIT-MP1
- MAGMA 5: 10:00 - 11:00
- Coffee break: 11:00 - 11:30
- MAGMA 6: 11:30 - 12:30
- Closing remarks: 12:30 onwards

Who Should Attend?
These lectures are perfect for students specializing in Algebraic graph theory, young PhDs, postdocs, and anyone interested in cryptography!
 

 
Don't miss out on this fantastic opportunity!


 

Datum in ura / Date and time: 8.4.24
(15:00-16:00)
Predavalnica / Location: FAMNIT-MP1
Predavatelj / Lecturer: Andrea Munaro (University of Parma)
Naslov / Title: Polynomial-time approximation schemes for induced subgraph problems on fractionally tree-independence-number-fragile graphs
Vsebina / Abstract:
 
We investigate a relaxation of the notion of fractional treewidth-fragility, namely fractional tree-independence-number-fragility. In particular, we obtain polynomial-time approximation schemes for meta-problems such as finding a maximum-weight sparse induced subgraph satisfying a given CMSO_2 formula on fractionally tree-independence-number-fragile graph classes. Our approach unifies and extends several known polynomial-time approximation schemes on seemingly unrelated graph classes, such as classes of intersection graphs of fat objects in a fixed dimension or proper minor-closed classes. We also study the related notion of layered tree-independence number, a relaxation of layered treewidth, and its applications to exact subexponential-time algorithms.
 
Joint work with Esther Galby and Shizhou Yang.